A circle with circumference 8, has an arc with a 288 degree central angle. What is the length of the arc?

2 answers:

8 0

We know that
the circumference C=2*pi*r
C=8 units

if 360° (full circle) has a length of-----------> 8 units
288°---------------------------> x
x=288*8/360-------> x=6.4 units

the answer is
6.4 units

ValentinkaMS [17]2 years ago

8 0

Answer:
length of arc = 6.4 units

Explanation:
The length of the arc can be calculated using the following formula:
length of arc = 2π * radius * $\frac{angle}{360}$ 

Taking a look at the equation and comparing it with the given, we would find that:
2π*r is the equation for calculating the circumference.
We are given that the the circumference of the circle is 8 units
theta is the angle subtended by the arc = 288°

Substitute with the givens in the above equation to get the length of the arc as follows:
length of arc = 8 * $\frac{288}{360}$ 
length of arc = 6.4 units

Hope this helps :)

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